Question: Solve for $x$ and $y$ using elimination. ${-4x-y = -16}$ ${-3x+y = -5}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-7x = -21$ $\dfrac{-7x}{{-7}} = \dfrac{-21}{{-7}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-4x-y = -16}\thinspace$ to find $y$ ${-4}{(3)}{ - y = -16}$ $-12-y = -16$ $-12{+12} - y = -16{+12}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {-3x+y = -5}\thinspace$ and get the same answer for $y$ : ${-3}{(3)}{ + y = -5}$ ${y = 4}$